are you saying that (2) is false and should instead say:

2. If everyone knows that (1) is true and if ... — Michael

It's worse than your amended 2. It recurses endlessly.



There is a fundamental problem. Whatever condition you think is sufficient ((1) in your case), , everybody must know it, not just you. But not in the omniscient sense, you, the islander, must know everybody knows it. But if you prove that, that new thing you now know is an additional fact that everyone must know, and you have to know they know it, and everybody must know that, and ..

My last substantive reply he only replied to the first sentence, I suspected he didn't really read it

Did you read my last post? I don't want to repeat of you didn't.

I’m not. I’m explicitly saying that I don’t think it needs to be recursive. — Michael

If you are missing the need, you are missing it.

.You are missing the recursion.

Once your list is fully expanded, #1 knows a fact, call it A:

A: everybody knows that everybody knows guru can see blue.

Ok, #1 knows A. But then #1 realizes, everyone has to know A to proceed, not just me. Otherwise we cannot act in concert.

So, really #1 must establish a meta-fact, B:

B: everyone knows A.

So #1 goes though a longer expansion, and proves B. But then #1 realizes, wait, if I have to know B to proceed, everyone has to know it. So now really he has to establish

C: everyone knows B.

...

And so on.

Even in the case of two people, they are all distinct facts, all the way up. It's just that we lose our ability to mentally grasp them pretty fast.

But isn't it curious that in R I said "better (or more artistic)," and in your own posts you recognize that some art is more artistic? Usually if something is more artistic then we would say that it is better qualified to be art, so I don't see how you can so neatly separate identification vs. evaluation. Usually the definition of art is going to determine what is more or less artistic — Leontiskos

By saying "better (or more artistic)" you are conflating evaluation and identification. We identify art by whether it is artistic or not. If A is more qualified as art than B, A is more artistic than B. But this does NOT mean A is better than B. This is demonstrated by the meal example. Every 5 star Michelin meal is more artistic than salted oatmeal. But there are many 5 star Michelin meals I would rather eat oatmeal than them.

Why is the Michelin meal more artistic than the basic meal? — Leontiskos

Much more effort, intention, time, resources, and training was devoted to the Michelin meal, all to create an object very carefully honed to modify the mental state of the consumer of the meal in a very specific way

Why is the Rembrandt better than the frowny face? — Leontiskos

I do not have a grip on the better question, and doubt there can be an account independent of preference. To be sure, the Rembrandt is also vastly more artistic than A Foul Frown, which seriously confuses the question here. .

(A notable point of agreement here may be this: That which barely qualifies as art at all is much more likely to be mistaken for non-art than something which readily qualifies as art, and the person who makes a mistake with regard to the former is much less mistaken than the person who makes a mistake with regard to the latter.) — Leontiskos

Yes, we agree here.

Number blues A B C...

At n=3, A doesn't know B knows C sees a blue.
At n=4, A doesn't know B knows C knows D sees a blue.
And so on.
Of course, every permutation of these are true as well.

here's the more tricky part - what new information did the Guru give them that they didn't already have? — flannel jesus

This is the beating heart of the puzzle, if you can't answer this you don't understand the puzzle. It is not to synchronize, not to make the counterfactual work.

It is to make sure, not that everybody knows everybody sees a blue, but that everybody knows everybody knows everybody knows..., n-1 times, that everybody sees a blue.

N=0 nobody is a blue.
N=1 not everybody sees a blue.
N=2 everybody sees a blue, everybody does not know everybody sees a blue.
N=3 everybody knows everybody sees a blue, everybody does not know everybody knows everybody sees a blue.
N=4 everybody knows everybody knows everybody sees a blue, everybody does not know everybody knows everybody knows everybody sees a blue.

And so on.


In order to get started, so that the failure of anybody to leave is meaningful, all this must be known. And, for @Michael solution to work, all this must be known too. Only a truth telling guru communicating to everyone that indeed there is a blue can cut through this recursive epistemic conundrum.

Would it then follow that if we have a prepared food that is not art, and then someone adds salt to make it taste better, it has become art? I am not convinced that such a thing is correctly identified as art. — Leontiskos

I think it would be art. The addition of salt, and the quantity added, is an aesthetic choice designed to modify mental state, in this case taste perception. Our "artist" may have chosen pepper instead, or, to really go all out, both.

But note, I agree with P and Q, and so I acknowledge that some art is more artistic than others. This meal would be a minimal example of art, barely belonging to the category at all, probably not enough to identify as art in an everyday context. Compare with a 5 star Michelin meal, much more artistic (but not better) , and which most everyone would call art.

If that is the only characteristic in your definition of art, then it seems like better/worse could only be attributed to the degree of modification intended or else achieved. — Leontiskos

No, and here you are again conflating identification vs evaluation of art. My definition is only for identification, evaluation is an orthogonal problem.

Consider again the Michelin meal. There are many basic meals (meals only marginally artistic) I would much rather eat than many Michelin meals. Many basic meals are just better, to me. Yet, I easily acknowledge that all the Michelin meals are more artistic than all the basic meals.

There are no doubt many gourmands who would always prefer the Michelin meals. Me and the gourmands are at an impasse, we have no independent way of deciding which is better, and nor should we expect one. Yet, we can both happily accept that the Michelin meals are more artistic.

Do you hold that benzodiazepines are art? — Leontiskos

No. By "experience" I mean, experience by the five senses. The effect of a benzo is not in the taste, but requires absorption into the blood stream. Drugs are human creations designed to alter physical state (and this alteration in turn, may or may not alter mental state). I exclude this, the alteration must arise from the experience of the purported art, in the above sense of "experience".

Similar for food. Food allays hunger by altering physical state. But, most food is also designed to alter mental state by the experience of it's taste, appearance, and smell, and so most (prepared) food is also art.

It may be helpful to introduce R beside P and Q, which includes a more specific genus: — Leontiskos

Why is this helpful to the question of "what is art"? To be sure, I think a frowny face scrawled on printer paper with feces is worse than a Rembrandt, by any reasonable definition of "worse" here, so I also believe R.

So what do you think? Do you prefer P or ~P? — Leontiskos

You seem to have ascribed a fair amount of doctrine to me that I have not explicitly set forth.

I prefer P, Q.

Do you have an alternative understanding of art to offer? — Leontiskos

I do, and I've already offered it to you directly. Here is my current formulation:

Art is a human creation (in the loosest, most permissive sense) whose experience is designed to modify the mental state of the experiencer.

You will no doubt feel that mine is vastly too permissive, just as yours is vastly too restrictive to me. Yet we both believe P, Q.

The problem with yours is that you, like so many, conflate the question of "what is good art" with "what is art". Much of what you wrote just reads as a list of your opinions on good art. But that may well be what @Moliere is actually asking, and so I might be the one who is ot.

Actually Michael still keeps green:

1. As of right now, everyone has come to know that everyone knows that green sees blue through some means or another — Michael

So for this to be false, we must find some blue that can find some blue that they aren't sure knows green sees a blue.

How will you do this when n=100?

Hey no editing.

For (1) to be false, blue A must see blue B , and know that B sees blue C, but not know that B knows that C sees a blue.

This doesn't seem possible when n=100.

And yet, it is wildly unintuitive that (1) is false when n=100, or 1000, or 10000, or...

Yeah, I follow, there is definitely a case to be made. This puzzle has been confusing the fuck out of me. The core problem is, I think you understand, at what point is (1)?

n=3: no, every blue thinks it could be 2
n=4: no, every blue thinks it could be 3
n=5: no, every blue thinks it could be 4
...

My disagreement is that you need the guru to say something just to make the counterfactual work.

I no longer believe this either.

no

But there is NOT one blue eyed person. The logic just says, IF there is one blue eyed person, he would leave. He did not, therefore there is not one blue eyed person.

I acknowledge it. But not that it is relevant to the counterfactual logic.

If there were only one blue, then it WOULDN'T be true that everyone sees at least one blue. — flannel jesus

A = Only one Blue
B = Everyone sees one blue
C = Blue leaves on first night

B
A -> ~B
A -> C

Still valid.

It doesn't work, precisely because this is the counterfactual situation in which the speaking is absolutely necessary because the hypothetical solitary blue does not see blue and has to be told in order to deduce their eye colour. This produces a contradiction that the hypothetical solitary blue cannot but does see blue, and cannot but does know their own eye colour. — unenlightened

I'm not sure about this.
If we take as a premise that "everyone sees at least one blue", then the counterfactual still works: If there is one blue, he would leave on day one. As you pointed out, that the counterfactual is false is irrelevant.

What if the sage had said instead, "I see at least two blues"?

This is just what I was talking about. It seems so damn reasonable that at some n, they could skip the stupid guru, lock eyes, and start from there. Like, suppose the universe was packed tight with 10^100 blues, you need a guru to tell you that... she sees a blue??? Yet, afaict, you do.

if they were perfect logicians then they wouldn't have been there for endless years; — Michael

Since they are perfect logicians, anything that would have allowed them to synchronize and leave before the guru spoke can be ruled out, since they are still there.

So it's explicit that everyone can see everyone else and knows that everyone can see everyone else, and implicit that new people don't just randomly appear or disappear — Michael

Ît does say

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. — flannel jesus

Maybe they were literally there forever.

A3 only works if you know that the blue eyed person you see knows green sees blue. But you don't know that he knows that. — flannel jesus

When b>=3, you absolutely DO know that. You can prove that everyone (including a real or hypothetical green) sees blue. The problem I see with @Michael reasoning is the use of "days". Days from what? There is a hidden assumption that everyone arrives at the island at the same time, and can all see each other at that time.

having examples where most people's "clearly" feelings are off base at least forces everyone to be a little more rigorous in their reasoning than just "it feels wrong". — flannel jesus

I mean, maybe, if everyone went through this problem, or similar, and perfectly internalized that lesson. But, they won't, and frankly we will probably forget this too, sooner or later. But the deeper quandary to me is, how can we ever really be certain? No matter how rigorous we are, or think we are, there can always be some error.

This is a stark example, but there have definitely been others, where it felt like something clearly was one way, when it turned out to be another. Surely you have experienced this as well, that the "clearly" feeling just isn't as reliable as it feels.

You just have to accept that you aren't a perfect logician. Is that so bad? — flannel jesus

The point is, usually when things feel logically certain, we think we at least know that much. That feeling of logical certainty amounts to a kind of psychological "proof". How else do we ultimately know anything logically follows?

Here, I was tripped up by the idea that the guru can't possibly be giving new information. But, amazingly, despite that feeling, she is, no matter how many blue eyed people there are.

Of course this forum, and philosophy in general, is a quagmire of mistakes. But it is probably much worse than we suspect. If our intuitions are that uncertain, even when they feel totally certain, it seems we are always on logical quicksand.

When someone uses art they are always doing something that falls away from the fundamental telos of art. — Leontiskos

Some of the uses of art I have in mind: mental stimulation. modulating mood. Experiencing intense emotions safely. Education. Passing the time. Having novel experiences.

Which of these is in accord with "the fundamental telos of art", and which is not?

When craftsmen create art for money, when painting was funded by patronage, when novelists and musicians aim to earn a living and even get rich, when entire industries are oriented around the production of art.. telos, or not the telos?

What are the stakes of abiding the telos, or of violating it? Where is the telos, who has defined it? Could it be... you?

You talk about intention as if there were only one of them, and we all agree on it. Art has one intention, to be appreciated for itself. Sex has one intention, pleasure. Why imagine this? It bears no resemblance to reality I can see.

And if hypericin wonders what verb is properly applied to art rather than 'use', then I would recommend 'appreciate' or 'enjoy'. In the case of a painting we might say 'gaze' or 'contemplate'. It would be strange to walk up to someone viewing a painting at a museum and ask if they are done using the piece.) — Leontiskos

Kind of like how food is useful for sustaining life, but we don't use it, we eat it?

Damn it. I buy it now. @unenlightenedhad it worked out before I even typed anything.

This brings up a related question I had thought of before: if it wasn't given in the question, I would have said, no one leaves, end of story. Even after seeing the answer, I had a hard time accepting it.

Given that cases like this exist, how do we even trust our own reasoning? I think the answer is, we can't (except maybe unenlightened!)

yeah that's the one I edited, I won't do that anymore.

I don't think so, but fair enough.

No, at b=2, every blue sees one other blue, and for all they know, that blue does not see a blue.

oh wait...

No, I was right, at b=2, a guru must see a blue, but it is not true that everyone else must also reach that conclusion. But at b=3, not only must everyone know that a guru must see a blue, everyone must arrive at the conclusion that everyone else knows that a guru must see a blue.

At b=3, everyone can make the guaranteed true statement, "everyone must see at least 1 blue"
At b=2 or b=1, this is not a true statement.
So at b=3, but not b=1 or b=2, anyone can say of the guru, "she could truly say, 'I see a blue'", and so anyone could say "if there were a guru, she would say, 'I see a blue'".

t's a counterfactual conditional from which valid deductions can be made thus:

If wishes were horses, then beggars would ride.
But beggars do not ride, but have to walk.
Therefore wishes are not horses. — unenlightened

It's a valid deduction, but we already know from the outset that wishes are not horses, it tells us nothing new. Similarly, the blue would have left if b=1, but we already know b>1, so their not leaving also tells us nothing new.



We agree that if b=1 or b=2, we MUST have the guru's statement to get the ball rolling. But if b>=3, then @Michael's reasoning seems to apply. We may as well just imagine the guru making the statement, which means we may as well just imagine the guru, and this imaginary guru can make the statement about blue or brown, and so everyone would have left long ago. But if this works with b>=3, surely it works with b=1 or b=2. But it does not.

Right? — flannel jesus

I mean yeah, but... but...

Why should the step "If there were one blue, they would leave on the first day" appear in the brains of perfect logicians who already knew before the guru spoke that this was not the case?

If that is not an active possibility, which it is not when blue >2, the failure of anyone to leave on the first night also provides no information.

Whereas if blue = 2, blue = 1 is still an active possibility, so its disconfirmation on the first night provides new information.

What's tripping me up is this:

If only one person has blue eyes, the guru's statement is clearly informative: the person with blue eyes doesn't see any blue eyes.

If only two people have blue eyes, the guru's statemen is clearly informative, since no one leaving rules out the 1st case for each of the two blue eyed people.

But at three people, the Guru may as well not have spoken. Everyone knows that there is at least one blue person, and everyone knows that everyone knows that there is at least one blue person. Once you move beyond two blue people, the scenario shifts, yet you are relying on the one and two blue people cases to reason about it.

Ok, this one is really tricky, and I couldn't figure it out on my own. But it is still not adding up for me, something is off.

From the start, everyone knows there is not just one person with blue eyes, so why are these perfect logicians waiting the first day?

From the start, everyone knows there is not just two people with blue eyes, so why are these perfect logicians waiting the second day?

...